Least-Resistance Consensus: Applying Via Negativa to Decision-Making ∗
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Least-Resistance Consensus: applying Via Negativa to decision-making ∗ Aleksander Kampa [email protected] July 2019 Abstract This paper introduces Least-Resistance Consensus (LRC), a cardinal voting system that focuses entirely on measuring resistance. It is based on the observation that our \negative gut feeling" is often a strong, reliable indicator and that our dislikes are stronger than our likes. Measuring resistance rather than acceptance is therefore likely to provide a more accurate gauge when a choice between multiple options has to be made. But LRC is not just a voting system. It encourages an iterative process of consensus- seeking in which possible options are proposed, discussed, amended and then either discarded or kept for a further round of voting. LRC also proposes to take the structure of group opinion into account, with a view not only to minimizing overall group resistance but also to avoiding, as much as possible, there being sizeable groups of strong dissenters. 1 Introduction In Western societies, the opinion that parliamentary democracy based on majority rule is the best possible form of government is widely held. We do know that minority opinions are not always represented and, as is the case in the UK with its first-past-the-post system, a party can gain an absolute majority with far fewer than half of the votes, but this seems to be considered a minor issue. Not just in government but at all levels of society, majority voting holds sway. Members of tribal societies in Africa and elsewhere, who are used to the lengthy and complex processes needed for reaching a wide consensus among community members, would probably call the idea of majority voting primitive. It might even be difficult to convince some of them that such a patently absurd concept is actually used by humans. Majority voting is, by its very nature, an antagonistic process. It is about one group winning a debate by sheer force of numbers: a more civilized version of \might is right". There are, of course, ∗Research supported by Fantom Foundation 1 alternatives to majority voting that offer more nuanced procedures, but most are influenced by the concept of majority voting. Also, there is always the underlying and unspoken positive bias: the focus is on identifying the best solution. It is the positive, the affirmative, that underpins most of Western thinking. In this paper, we will present the Least-Resistance Consensus (LRC) method, which focuses on determining which solution encounters the least resistance from a group. To begin with, however, we present a brief historical perspective of voting research. 2 Traditional Voting Systems 2.1 Some famous names in voting theory The question of fair voting is probably as old as humanity. Plato proposed a multi-stage voting process more than 2,000 years ago, and Pliny the Younger wrote about strategic voting in the Roman Senate around 100 AD, as noted in Szpiro [1]. Many famous people have worked on election methods: the Medieval polymath and mystic Ramon Llull, the philosopher and cardinal Nicolaus Cusanus, the scientist Pierre-Simon Laplace and the Reverend Charles Dodgson, better known by his pen name, Lewis Carroll. Two other names that are associated with the history of voting systems are the Marquis de Con- dorcet and Jean-Charles de Borda. They were contemporaries, and, indeed, the two traditional election systems are associated with their names. 2.2 The Condorcet and Borda methods Apart from simple majority-voting, the limitations of which have been recognised since Antiquity, two classical voting methods have emerged. The first approach consists of asking voters to compare all possible pairs of candidates successively. The candidate who wins the most head-to-head contests wins the election (there are various ways to handle ties). This method was initially described by Llull and was later proposed by Condorcet. It is now often referred as the Condorcet method [2] or Copeland's method [3]1. If one candidate wins all head-to-head contests, she is called the Condorcet winner. In the second approach, voters are asked to rank all candidates, with the lowest-ranked candidate given 1 point, the second-lowest two points, etc. The winner is the candidate with the highest Borda count, which is the sum of points received from all voters. This method, called Borda's method, was used in the Roman Senate \beginning around 105 AD" [4]; it was proposed by Cusanus to elect Holy Roman Emperors2 and reinvented by Borda. Neither of these approaches is without drawbacks. For example, the Condorcet method sometimes does not yield a winner or a consistent ordering of the candidates - this is known as the Condorcet paradox. With Borda's method, the withdrawal of even a low-ranked candidate can sometimes change the winner of the election. To overcome such problematic behaviours, many variations of the Condorcet and Borda methods have been devised, including multi-stage methods. None of these voting methods proved to be without flaws. A very accessible introduction to the problems and paradoxes of the traditional voting systems is given in Powers [5] and in chapter 3 of Balinksi and Laraki [6]. 1In fact, there are many variations of the Condorcet method, with Copeland's method being the simplest. 2His proposal was not adopted. 2 2.3 Arrow's impossibility theorem The reason why no perfect solution was ever found in the traditional setting became clear in 1951 when Kenneth Arrow published his famous impossibility theorem. Assume that voters are asked to (strictly) rank at least three candidates. We require a ranking function that ranks all candidates and satisfies the following criteria: A1. The function produces a ranking for all possible inputs (\unrestricted domain"); A2. if all voters prefer A to B, then A will rank higher than B (\unanimous decision"); A3. the relative rank of A and B does not depend on any other candidate (\independence of irrelevant alternatives", or IIA); A4. no single voter determines the outcome of the vote (\nondictatorial"). What Arrow proved is that such a function does not exist. For this and other work, he later received a Nobel prize in economics. The usual way of proving Arrow's theorem is to show that any ranking function satisfying A1, A2 and A3 is, in fact, equal to the ranking of one specific voter and ignores the input of all other voters, thus failing condition A4. See Geanakoplos [7] (3rd proof) for a short and extremely elegant proof; Fey [8] also provides a simple proof. Note that the impossibility holds even without requiring other conditions. For example, one desirable feature of a voting system is \monotonicity": placing a winning candidate higher should never cause that candidate to lose. So if there is a configuration where candidate A is ranked first by the ranking function and one or more voters place that candidate higher, then this should not cause A to be ranked lower. Several instant-runoff methods violate monotonicity. Another desirable feature is resistance to strategic manipulation. 2.4 A note on modern democracies The inconsistencies observed in various Condorcet and Borda voting systems are quite minor compared to seemingly unfair results seen in democracies that use first-past-the-post voting. In the 1983 UK general election, the Alliance of the Liberals and SDP received over 25% of the popular vote but won only 3.5% of the seats (23 out of 650) in Parliament. For Labour, 28% of the popular vote translated into 32% of the seats (209 seats), while the Conservatives received 42% of the vote and had an absolute majority of 61% of the seats in Parliament. In the 2007 presidential election in France, it is considered almost certain that Fran¸coisBayrou would have won one-to-one against any of the other candidates. But because Bayrou did not advance to the second round, Nicolas Sarkozy became president. In the 2015 UK general election, Labour added 0.74 million voters but lost 26 seats. The Conser- vatives gained 24 seats while adding only 0.63 million voters and obtained a slim parliamentary majority. UKIP received 12.6% of the popular vote but ended up with only one of 650 seats in Parliament - a mere 0.15%. It is interesting, and somewhat puzzling, to note that the Condorcet and Borda methods, whatever their flaws, are often superior to voting methods used in some democratic countries today. 3 From ordinal to cardinal voting In their book \Majority Judgement", published in 2010, Balinski and Laraki argue that voting theory should be looking beyond traditional methods ([6] p. 56): Perhaps the most astonishing aspect of the theory of voting is that despite Arrow's celebrated impossibility theorem and others, the search for a best method has continued 3 within the basic framework first conceived by Llull and Cusanus almost a millennium ago (...) We already know that plurality voting is highly problematic. Ordinal voting, which ranks candi- dates, is better but also flawed. We need to focus on cardinal voting, which evaluates candidates3 rather than ranking them. The question is: why has it taken so long for this realisation to sink in? Arrow explicitly rejected cardinal utility in his famous book, Social Choice and Individual Values, which was published in 1951. Only two years later, however, Harsanyi, also a future Nobel prize winner, made a strong case for cardinal utility [9], and in 1955 essentially showed that Arrow's impossibility theorem does not hold when cardinal utility is used [10]. Writing in 2005, Hillinger [11] provides interesting background information and describes how Arrow, as well as others, failed to take much notice of Harsanyi's work for decades { even though Arrow was Harsanyi's thesis advisor! Hillinger concludes his historical perspective by writing: Given the long history of voting theory, it is surprising that the first step towards UV4, in the form of AV5, was taken as late as the 1970s and the second step, the introduction of a scale with arbitrary divisions, was taken in 2000 with Smith's paper on RV6.